For a few days I've tried to wrap my head around the functional programming paradigm in Haskell. I've done this by reading tutorials and watching screencasts, but nothing really seems to stick.
Now, in learning various imperative/OO languages (like C, Java, PHP), exercises have been a good way for me to go. But since I don't really know what Haskell is capable of and because there are many new concepts to utilize, I haven't known where to start.

So, how did you learn Haskell? What made you really "break the ice"? Also, any good ideas for beginning exercises?

15 Answers
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I'm going to order this guide by the level of skill you have in haskell, going from an absolute beginner right up to an expert. Note that this process will take many months (years?), so it is rather long.

Absolute Beginner

Firstly, haskell is capable of anything, with enough skill. It is very fast (behind only c and c++ in my experience), and can be used for anything from simulations to servers, guis and web applications.

However there are some problems that are easier to write for a beginner in haskell than others. Mathematical problems and list process programs are good candidates for this, as they only require the most basic of haskell knowledge to be able to write.

Firstly, some good guides to learning the very basics of haskell are the happy learn haskell tutorial and the first 6 chapters of learn you a haskell. While reading these, it is a very good idea to also be solving simple problems with what you know.

A good list of problems to try is the haskell 99 problems page. These start off very basic, and get more difficult as you go on. It is very good practice doing a lot of those, as they let you practice your skills in recursion and higher order functions. I would recommend skipping any problems that require randomness as that is a bit more difficult in haskell. Check this SO question in case you want to test your solutions with QuickCheck (see Intermediate below).

Once you have done a few of those, you could move on to doing a few of the Project Euler problems. These are sorted by how many people have completed them, which is a fairly good indication of difficulty. These test your logic and haskell more than the previous problems, but you should still be able to do the first few. A big advantage haskell has with these problems is Integers aren't limited in size. To complete some of these problems, it will be useful to have read chapters 7 and 8 of learn you a haskell as well.

Beginner

After that you should have a fairly good handle on recursion and higher order functions, so it would be a good time to start doing some more real world problems. A very good place to start is Real World Haskell (online book, you can also purchase a hard copy). I found the first few chapters introduced too much too quickly for someone who has never done functional programming/used recursion before. However with the practice you would have had from doing the previous problems you should find it perfectly understandable.

Working through the problems in the book is a great way of learning how to manage abstractions and building reusable components in haskell. This is vital for people used to object-orientated (oo) programming, as the normal oo abstraction methods (oo classes) don't appear in haskell (haskell has type classes, but they are very different to oo classes, more like oo interfaces). I don't think it is a good idea to skip chapters, as each introduces a lot new ideas that are used in later chapters.

After a while you will get to chapter 14, the dreaded monads chapter (dum dum dummmm). Almost everyone who learns haskell has trouble understanding monads, due to how abstract the concept is. I can't think of any concept in another language that is as abstract as monads are in functional programming. Monads allows many ideas (such as IO operations, computations that might fail, parsing,...) to be unified under one idea. So don't feel discouraged if after reading the monads chapter you don't really understand them. I found it useful to read many different explanations of monads; each one gives a new perspective on the problem. Here is a very good list of monad tutorials. I highly recommend the All About Monads, but the others are also good.

Also, it takes a while for the concepts to truly sink in. This comes through use, but also through time. I find that sometimes sleeping on a problem helps more than anything else! Eventually, the idea will click, and you will wonder why you struggled to understand a concept that in reality is incredibly simple. It is awesome when this happens, and when it does, you might find haskell to be your favorite imperative programming language :)

To make sure that you are understanding Haskell type system perfectly, you should try to solve 20 intermediate haskell exercises. Those exercises using fun names of functions like "furry" and "banana" and helps you to have a good understanding of some basic functional programming concepts if you don't have them already. Nice way to spend your evening with list of paper covered with arrows, unicorns, sausages and furry bananas.

Intermediate

Once you understand Monads, I think you have made the transition from a beginner haskell programmer to an intermediate haskeller. So where to go from here? The first thing I would recommend (if you haven't already learnt them from learning monads) is the various types of monads, such as Reader, Writer and State. Again, Real world haskell and All about monads gives great coverage of this. To complete your monad training learning about monad transformers is a must. These let you combine different types of Monads (such as a Reader and State monad) into one. This may seem useless to begin with, but after using them for a while you will wonder how you lived without them.

Now you can finish the real world haskell book if you want. Skipping chapters now though doesn't really matter, as long as you have monads down pat. Just choose what you are interested in.

With the knowledge you would have now, you should be able to use most of the packages on cabal (well the documented ones at least...), as well as most of the libraries that come with haskell. A list of interesting libraries to try would be:

Parsec: for parsing programs and text. Much better than using regexps. Excellent documentation, also has a real world haskell chapter.

Quickcheck: A very cool testing program. What you do is write a predicate that should always be true (eg length (reverse lst) == length lst). You then pass the predicate the quickCheck, and it will generate a lot of random values (in this case lists) and test that the predicate is true for all results. See also the online manual.

gtk2hs: The most popular gui framework for haskell, lets you write gtk applications in haskell.

happstack: A web development framework for haskell. Doesn't use databases, instead a data type store. Pretty good docs (other popular frameworks would be snap and yesod).

Also, there are many concepts (like the Monad concept) that you should eventually learn. This will be easier than learning Monads the first time, as your brain will be used to dealing with the level of abstraction involved. A very good overview for learning about these high level concepts and how they fit together is the Typeclassopedia.

Applicative: An interface like Monads, but less powerful. Every Monad is Applicative, but not vice versa. This is useful as there are some types that are Applicative but are not Monads. Also, code written using the Applicative functions is often more composable than writing the equivalent code using the Monad functions. See Functors, Applicative Functors and Monoids from the learn you a haskell guide.

Monoid: A Monoid is a type that has a zero (or mempty) value, and an operation, notated <> that joins two Monoids together, such that x <> mempty = mempty <> x = x and x <> (y <> z) = (x <> y) <> z. These are called identity and associativity laws. Many types are Monoids, such as numbers, with mempty = 0 and <> = +. This is useful in many situations.

Arrows: Arrows are a way of representing computations that take an input and return an output. A function is the most basic type of arrow, but there are many other types. The library also has many very useful functions for manipulating arrows - they are very useful even if only used with plain old haskell functions.

ST Monad: lets you write code with a mutable state that runs very quickly, while still remaining pure outside the monad. See the link for more details.

FRP: Functional Reactive Programming, a new, experimental way of writing code that handles events, triggers, inputs and outputs (such as a gui). I don't know much about this though. Paul Hudak's talk about yampa is a good start.

There are a lot of new language features you should have a look at. I'll just list them, you can find lots of info about them from google, the haskell wikibook, the haskellwiki.org site and ghc documentation.

While learning all these new libraries and concepts, it is very useful to be writing a moderate-sized project in haskell. It can be anything (eg a small game, data analyser, website, compiler). Working on this will allow you to apply many of the things you are now learning. You stay at this level for ages (this is where I'm at).

Expert

It will take you years to get to this stage (hello from 2009!), but from here I'm guessing you start writing phd papers, new ghc extensions, and coming up with new abstractions.

Getting Help

Finally, while at any stage of learning, there are multiple places for getting information. These are:

the #haskell irc channel

the mailing lists. These are worth signing up for just to read the discussions that take place - some are very interesting.

other places listed on the haskell.org home page

Conclusion

Well this turned out longer than I expected... Anyway, I think it is a very good idea to become proficient in haskell. It takes a long time, but that is mainly because you are learning a completely new way of thinking by doing so. It is not like learning ruby after learning java, but like learning java after learning c. Also, I am finding that my object-orientated programming skills have improved as a result of learning haskell, as I am seeing many new ways of abstracting ideas.

Yay arrows! First you let monads shape your brain, then you stand on your head and think about comonads, and then you do both at the same time to get arrows :) There's a lot of expressive power in Haskell that can be opened up with type-level programming, too.
– ephemientJul 6 '09 at 18:17

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@nanothief Monad is more powerful, but also less compositional... a lot of people use monads where they could've gotten away with cleaner Applicative code. Most things that are Functors are also Monads, but you don't go around using >>= and return when fmap will suffice, because the latter leads to much simpler code if you can use it.
– Tom CrockettMar 16 '11 at 8:21

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@pelotom, I've added the typeclassopedia link as well as a better reasons to use Applicative to that section, and removed the Functor section. It is hard getting the Monad and Applicative concepts in the right order since of the emphasis on Monads in most teaching material (including RWH). On the other hand, the teach you a haskell tutorial has come a long way since I initially wrote the answer (nearly 2 years :O), and does teach Applicative before Monad, perhaps that should now be the recommended way of learning haskell.
– David MianiMar 18 '11 at 4:48

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Great advice. I started this over a year ago, and am most of the way through the Intermediate stage. Feedback: RWH's monad chapter (chapter 14) is poorly explained. Reading the online version of RWH is beneficial, because it contains crowdsourced comments which aid the chapter. FWIW, You Could Have Invented Monads, was the monad tutorial that worked best for me.
– TomMay 9 '14 at 10:32

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@tomf: Thanks! I've always been amazed at how well this answer has done - it has nearly been five years since I wrote it but it is still going strong. I will need to do an update to it soon though, as it is a bit out of date. It doesn't mention lenses, pipes, constraint kinds, the haskell platform, type level numbers, and they are pretty major new topics since this was written. You are right that RWH isn't as good anymore, it hasn't been updated in a long time and a lot of the examples aren't compiling. I'm glad it was still helpful to you anyway.
– David MianiMay 9 '14 at 11:39

I started with this, but my opinion is that you should go directly to Real World Haskell. The difference is like learning C from K&R or "C for dummies" which tries to be simple, but misses important stuff with its approach. I think it's better to just get the facts straight instead of trying to learn Haskell "the imperative way".
– John SmithJun 18 '09 at 13:32

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I absolutely LOVE this, and I have invested a lot of time into this and Real World Haskell. IMO, "Learn You a Haskell" gives deeper insight than Real World Haskell, though they're both great resources.
– Charlie FlowersMar 11 '10 at 5:29

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@abababa22 I think reading LYAH first and then going to RWH is the best idea. LYAH doesn't teach you just Haskell; it teaches you functional programming. You begin thinking in functional way when you solve problems. Clearly, only LYAH wouldn't be enough to write a large application, but it bends your mind the right way. If you're from imperative background, this is the best way, IMO
– Abdulsattar MohammedNov 24 '11 at 6:55

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@Telemachus Just to note: the PDF is not the final version, at least it is missing the last chapter.
– sdcvvcMay 20 '13 at 21:57

Most of the Haskell programs I've done have been to solve Project Euler problems.

Once piece of advice I read not too long ago was that you should have a standard set of simple problems you know how to solve (in theory) and then whenever you try to learn a new language you implement those problems in that language.

Real World Haskell in my experience is great, until you reach chapter 5. From then on I wouldn't recommend it.
– MasterMasticApr 17 '14 at 7:19

Why @MasterMastic? What is the problem beyond chapter 5? I'd like to know before I spend the money.
– Jay BlanchardMay 5 '14 at 17:49

@JayBlanchard In chapter 5 you start getting a concrete example of a library, which is nice, but they tell you what they're going to do, do it, but they do not explain why entirely, and not clearly at all, and there's quite a bit of magic hex literals. You're just going through the motions. That wasn't the biggest issue for me tho, the biggest issue was that the book heavily depends on those kind of hard and long examples (long enough to take more than an entire chapter). You can hardly just read the parts you want to. I think great authors, amazing knowledge but extremely poor execution.
– MasterMasticMay 5 '14 at 18:28

To add on others' answers - there is one useful that will help you when coding (for example when solving project Euler problems):
Hoogle. You can use either the command line interface or the web interface.

Command Line

After you installed the Haskell platform be sure to cabal install hoogle

Hoogle usage example:

You have a function f x = 3 * x + 1 and you want to apply it on (5 :: Int), then apply it on the result and on that result and so on and get an infinite list of those values. You suspect there might already exist a function to assist you (not specifically for your f though).

That function would be of type (a -> a) -> a -> [a] if it takes f 5 or a -> (a -> a) -> [a] if it takes 5 f (we assume the function is for general types and not just Ints)

Graham Hutton's Programming in Haskell is concise, reasonably thorough, and his years of teaching Haskell really show. It's almost always what I recommend people start with, regardless of where you go from there.

In particular, Chapter 8 ("Functional Parsers") provides the real groundwork you need to start dealing with monads, and I think is by far the best place to start, followed by All About Monads. (With regard to that chapter, though, do note the errata from the web site, however: you can't use the do form without some special help. You might want to learn about typeclasses first and solve that problem on your own.)

This is rarely emphasized to Haskell beginners, but it's worth learning fairly early on not just about using monads, but about constructing your own. It's not hard, and customized ones can make a number of tasks rather more simple.

This is a totally under-appreciated book (and answer). The chapter on functional parsers, followed by a chapter on IO, neither of which even mention monads, really shines as an elegant pedagogical approach.
– michiakigJul 16 '12 at 16:27

I'd suggest joining the #haskell irc channel and asking questions there. That's how I learned Haskell. If you go through Real World Haskell as suggested above, real time answers to your questions will help greatly. Lots of smart people on #haskell write Haskell for fun and for profit, so you'll get lots of good input. Try it!

Another good learning resource (probably on the intermediate level), which has helped me a lot and hasn't been mentioned in the other answers as far as I can see, is Brent Yorgey's Typeclassopedia, which can be found in The Monad Reader (Issue 13)

It is written in a very accessible style and contains (among many other things), the following introductory advice:

There are two keys to an expert Haskell hacker’s wisdom:

Understand the types.

Gain a deep intuition for each type class and its relationship to other
type classes, backed up by familiarity with many examples.

The Monad Reader itself is an absolute treasure trove for functional programmers (not only Haskell programmers).

If you only have experience with imperative/OO languages, I suggest using a more conventional functional language as a stepping stone. Haskell is really different and you have to understand a lot of different concepts to get anywhere. I suggest tackling a ML-style language (like e.g. F#) first.

Elm might be the closest, more usefule and beginner-friendly of these alternatives...
– Pedro Morte RoloDec 8 '16 at 21:22

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I disagree on passing by thru a temporary route, like F#. For me, it's like drinking a vodka you have to sip it in quickly. More painful that way, but pleasure is also there. Temporary routes, only leads to more confusion for me.
– ifelsemonkeyAug 22 at 10:32

Sorry but using the PhD argument here is like saying you have to have a 300$ kitchen knife to be a good chef. Even Simon Peyton Jones - the father of Haskell - does not have a PhD. Practice and persistence is what leads to expertise both here and in any other field.
– Petras PurlysJul 17 at 13:30

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